Question

The differential equation \( \frac{dy}{dx} + x = A \) (where A is constant) represents:

• A. A family of circles having centre on the x-axis
• B. A family of circles having centre on the y-axis
• C. A family of all circles having centre at the origin
• D. A family of ellipses
• E. A family of hyperbolas

Hint:

For equations of circles, look for forms that resemble the general equation \( (x - h)^2 + (y - k)^2 = r^2 \).

Answer 1

The Correct Option is A

This differential equation represents a family of circles where the value of A defines the radius of each circle, and the centres lie on the x-axis.